Discussion
When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is
Answer: B
The probability is \(\frac{5}{324}\).
Six dice have \(6^{6} = 46656\) equally likely outcomes. All six faces appear exactly once in \(6! = 720\) of them, one for each ordering of the numbers 1 to 6 over the dice.
\[ P = \frac{720}{46656} = \frac{5}{324} \approx 0.0154 \]
\(\frac{1}{324}\) undercounts the orderings by a factor of 5, and \(\frac{7}{324}\) and \(\frac{11}{324}\) do not reduce from \(6!/6^{6}\).
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